证明数列1+1/3+1/5+…+1/(2n+1)-0.5*ln(n+1)有极限
问题描述：
证明数列1+1/3+1/5+…+1/(2n+1)-0.5*ln(n+1)有极限
答
设f(n)=1+1/3+1/5+…+1/(2n+1)-0.5*ln(n+1)
f(n+1)-f(n)=1/(2n+3)-0.5*ln(n+2)+0.5*ln(n+1)
=1/(2n+3)-0.5*ln(1+1/(n+1))
下面证明ln(1+x)>x/(x+1) (0